What percent is the change in the price if: The price was $100 and now it is $1250?

Answer: The measure of Angle A is 46 degrees.

Step-by-step explanation:

Complementary angles are angles that when both added together are equal to 90 degrees. So the measure of angle A plus the measure of angle B is equal to 90 or 3x - 2 + 2x + 12 = 90. Add like terms so you get 5x + 10 = 90. Subtract 10 on both sides you get 5x = 80. Divide by 5 on both sides and you get x = 16. To find the measure of angle A, plug in your x value. So M<A = 3(16) - 2. Ange A is equal to 46. I double checked my answer too and plugged my x value into M<B and got 44. So indeed 44 + 46 = 90.

Answer:

2, 8, 4, 16, 12, 30, 26, 50

Step-by-step explanation:

The first is determinate the different (\(d\)) between each consecutive value (\(a_n - a_{n-1}\)).

\(8 - 2 = 6\\4 - 8 = -4\\16 - 4 = 12\\12 - 16 = -4\\\)

How you can see when the position of the number in the sequence is odd you have to sum a number \(6x\) and when the position of the number in the sequence is a even number you have to substract -4.

Why \(6x\)? If you see the first two odd position numbers in the sequence are multiples of 6, then we made the deduction that each time that you sum a number this is a multiply of 6 and -4 is constant for each position even number.

Then for each odd position number in the sequence it's representation is of the form:

\(a_{n-1} + 6x = a_n\)

Where \(a_{n-1}\) is the number of before, \(x\) the odd position of the number in the sequence and \(a_n\) is the current value of \(a_n\)

So the rest of the sequence is of the next form:

\(12 + 6(3) = 30\)

\(30 -4 = 26\)

\(26 + 6(4) = 50\)

So the final answer is \(\{30, 26, 50\}\)

Answer:

It's in the air for about 2 seconds (A), maximum height was about 17 feet, and yes you win the price since 17> 15.

Step-by-step explanation:

Note that based on probabilities,

The expected number of Democrats on the committee is 5.

The expected number of states represented on the committee is 26.

The expected number of states such that both of the state's senators are on the committee is 9.09.

a)  The probability that a randomly chosen senator is a Democrat is 50/100 = 1/2.

So, the expected number of Democrats on a committee of size 10 is

1/2 * 10 = 5.

b) The minimum number of   states that can be represented on a committee of size 10 is 2, and the maximum numberis 50.

The expected number of states representedon the committee is the average of these two values, which is (2 + 50)/  2 = 26.

c)  There are 50 states, and each state has 2 senators. So, there are a total of 100 pairs of senators.

The probability that a randomly chosen pair of senators both belong to the same state is 50/100 * 49/99

= 1/11.

The expected number of states such that both of the state's senators are on the committee is 100 * 1/11 = 9.09.

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Answer:

D

Step-by-step explanation:

Based on the information on the number line, the numbers that represent the percentages are: 42 (100%), 21 (50%), 63 (150%).

To calculate the number that is equivalent to each percentage we must carry out the following procedure: Rule of three. In this case we must take into account that 42 represents 100% of the people.

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Answer:

$36

Step-by-step explanation:

1. Determine the surface area of the  largest jaw breaker

Surface area of a sphere = 4πr²

4 x 3.14 x 2² = 50.24in²

2. Determine the surface area of the new jaw breaker

4 x 3.14 x 6² = 452.16 in²

3. Determine the cost per area

4/ 50.24

4. Determine the price for the new jaw breaker

4/ 50.24 x 452.16 = $36

The following can be shown about the diagonals of parallelogram PQRS to compare the proof that diagonals of a parallelogram bisect each other: B. PR and SQ have the same midpoint.

In Mathematics and Geometry, a parallelogram is a geometrical figure (shape) and it can be defined as a type of quadrilateral and two-dimensional geometrical figure that has two (2) equal and parallel opposite sides.

In order for any quadrilateral to be considered as a parallelogram, two pairs of its parallel opposite sides must be equal (congruent). This ultimately implies that, the diagonals of a parallelogram would bisect one another only when their midpoints are the same:

(Line segment PR)/2 = (Line segment SQ)/2

Line segment PR = Line segment SQ

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Hi there!

\(\large\boxed{\text{p(x) = 4(3)^{x}, q(x) = 4(2)^{x}}}\)\(\large\boxed{p(x) = 4(3)^{x}}}\\\large\boxed{ q(x) = 4(2)^{x}}\)

(a)

Looking at the graphs, we see that both p(x) and q(x) intersect the y-axis at

y = 4, or (0, 4).

(b)

The base of the functions is simply the value of the y-intercept, or a = 4.

(c)

We can write equations for both using an external point at x = 1:

p(x):

y = 4(b)^x

Plug in the point (1, 12) to solve:

12 = 4(b)^1

12 = 4b

b = 3

Rewrite the equation:

\(p(x) = 4(3)^{x}\)

q(x):

y = 4(b)^x, plug in the point (1, 8):

8 = 4(b)^1

8 = 4b

b = 2

Rewrite:

\(q(x) = 4(2)^{x}\)

Factoring an equation is the process of finding the common factors that multiply to give the terms in the equation. It is a fundamental skill in algebra and is used to simplify equations, solve equations, and find solutions to problems.

In this example, we have factored the equation by using the distributive property in reverse. We have removed the product of (x+4)(x+2) from both sides of the equation. This is a very common method of factoring equations.

Another way to factor an equation is to use the difference of squares method. For example, x^2 - 25 = (x+5)(x-5).

A third method is to factor by grouping. For example, x^3 + 4x^2 -4x - 16 = (x^3 + 4x^2) - (4x + 16) = x(x^2 + 4x) -4(x + 4).

It's also important to note that not all equations can be factored. In some cases, you may need to use other methods such as completing the square or using the quadratic formula to solve the equation.

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On solving the provided question, we can say that in the quadrilateral BD = 11, BC = 8, DC = 8 and perimeter of ABCD is = 38

A quadrilateral is a four-sided polygon in geometry that has four edges and four corners. The word is a derivative of the Latin words quadri and latus (meaning "side"). Having four sides, four vertices, and four corners, a rectangle is a two-dimensional form. Concave and convex come in primarily two varieties. Additionally, there are several subclasses of convex quadrilaterals, including trapezoids, parallelograms, rectangles, rhombuses, and squares. Four straight sides make up a rectangle, which is a two-dimensional form. There are several different types of quadrilaterals, including parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.

in the quadrilateral

BD = 11 ( equal angle have equal sides)

BC = 8

DC = 8

perimeter of ABCD is = 38

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Answer:

36

Step-by-step explanation:

A dentist bought 9 bags of prizes for his patients.

Each of the bags has 12 prizes

The first step is to calculate the total number of prizes

= 9 × 12

= 108 prizes

Since the prizes will be shared equally in 3 boxes then the number of prizes in each box can be calculated as follows

= 108/3

= 36

Hence the number of prizes in each of the 3 boxes is 36

Answer:

Step-by-step explanation:

We can interpret this as:

Calculation is:

Translate this into the given format:

This matches option C

it displays the computed sum and product of the diagonal elements.

Here's a MATLAB code to find the sum and product of the diagonal elements of a given matrix `A`, as well as an example execution for `A = ones(5)`:

```matlab

% Define the matrix A

A = ones(5);

% Get the size of the matrix

[n, ~] = size(A);

% Initialize variables for sum and product

diagonal_sum = 0;

diagonal_product = 1;

% Calculate the sum and product of diagonal elements

for i = 1:n

   diagonal_sum = diagonal_sum + A(i, i);

   diagonal_product = diagonal_product * A(i, i);

end

% Display the results

disp("Sum of diagonal elements: " + diagonal_sum);

disp("Product of diagonal elements: " + diagonal_product);

```

Example execution for `A = ones(5)`:

```

Sum of diagonal elements: 5

Product of diagonal elements: 1

```

In this example, `A = ones(5)` creates a 5x5 matrix filled with ones. The code then iterates over the diagonal elements (i.e., elements where the row index equals the column index) and accumulates the sum and product. Finally, it displays the computed sum and product of the diagonal elements.

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The percentage of the reservations were for Friday or Saturday is 67%

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we have the following data values for reservation

The total number of reservations in the bar chart is then calculated as

Total number of reservations = 5 + 3 + 4 + 7 + 26 + 30 + 9

Evaluate the sum

So, we have the following representation

Total number of reservations = 84

The total number of reservations for Friday or Saturday is then calculated as

Total number for Friday or Saturday = 26 + 30

Evaluate the sum

So, we have the following representation

Total number for Friday or Saturday = 56

The percentage of the reservations were for Friday or Saturday is then calculated as

Percentage = Total number for Friday or Saturday/Total number of reservations

This gives

Percentage = 56/84

Evaluate

Percentage = 67%

Hence, the percentage is 67%

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Answer:

the answer would be 14-16=-2

Step-by-step explanation:

first u look where the first long arrow goes on this problem then you follow the second arrow which stops at 6 then u count how much until negative 2. but how I did it is the form 14 how much to 0 which is 14 the I count how many until I get to -2 and there's the answer

The one-sided limits at x = 0 are:                                                                                                                                                          lim f(x) = 0, as x approaches 0 from the left (x → 0-)

lim f(x) = 3, as x approaches 0 from the right (x → 0+)

The function f(x) is defined as:

f(x) = { 3, if x > -4

{ Ø, if x = -4

{ 0, if x < -4

To find the one-sided limits at x = 0, we need to evaluate the function from the left and the right of x = 0.

a. The left-hand limit at x = 0 is:

lim f(x) = lim 0 = 0

x → 0-

Since x < -4 implies that f(x) = 0, the function approaches 0 from the left-hand side.

b. The right-hand limit at x = 0 is:

lim f(x) = lim 3 = 3

x → 0+

Since x > -4 implies that f(x) = 3, the function approaches 3 from the right-hand side.

Therefore, the one-sided limits at x = 0 are:

lim f(x) = 0, as x approaches 0 from the left (x → 0-)

lim f(x) = 3, as x approaches 0 from the right (x → 0+).

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A scale that allows us to rank individuals or objects, but not say anything about the meaning of the differences between the ranks, is an ordinal scale.

Therefore, a scale that allows us to rank individuals or objects, but not say anything about the meaning of the differences between the ranks, is an ordinal scale.

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The solution to the provided differential equation with the initial condition y(0) = 5 and u as a step change of unity is y = -2

The provided differential equation is: \(\[\frac{{dy}}{{dt}} = y + 2u\]\) with the initial condition: y(0) = 5 where u is a step change of unity.

To solve this differential equation, we can use the method of integrating factors.

First, let's rearrange the equation in the standard form:

\(\[\frac{{dy}}{{dt}} - y = 2u\]\)

Now, we can multiply both sides of the equation by the integrating factor, which is defined as the exponential of the integral of the coefficient of y with respect to t.

In this case, the coefficient of y is -1:

Integrating factor \(} = e^{\int -1 \, dt} = e^{-t}\)

Multiplying both sides of the equation by the integrating factor gives:

\(\[e^{-t}\frac{{dy}}{{dt}} - e^{-t}y = 2e^{-t}u\]\)

The left side of the equation can be rewritten using the product rule of differentiation:

\(\[\frac{{d}}{{dt}}(e^{-t}y) = 2e^{-t}u\]\)

Integrating both sides with respect to t gives:

\(\[e^{-t}y = 2\int e^{-t}u \, dt\]\)

Since u is a step change of unity, we can split the integral into two parts based on the step change:

\(\[e^{-t}y = 2\int_{{-\infty}}^{t} e^{-t} \, dt + 2\int_{t}^{{\infty}} 0 \, dt\]\)

Simplifying the integrals gives:

\(\[e^{-t}y = 2\int_{{-\infty}}^{t} e^{-t} \, dt + 0\]\)

\(\[e^{-t}y = 2\int_{{-\infty}}^{t} e^{-t} \, dt\]\)

Evaluating the integral on the right side gives:

\(\[e^{-t}y = 2[-e^{-t}]_{{-\infty}}^{t}\]\)

\(\[e^{-t}y = 2(-e^{-t} - (-e^{-\infty}))\]\)

Since \(\(e^{-\infty}\)\) approaches zero, the second term on the right side becomes zero:

\(\[e^{-t}y = 2(-e^{-t})\]\)

Dividing both sides by \(\(e^{-t}\)\) gives the solution: y = -2

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If side of square is (x-1) units, and the dimensions of rectangle are x units by (x-2) units, then

(a) the possible values are : all real number greater than 2,

(b) Square has a greater area than rectangle,

(c) The difference in area is 1 unit.

Part (a) : To be a valid square, the sides must have the same length. So, we equate expression for length of each side of square equal to each other and solve for x:

x - 1 = x - 1

0 = 0

This equation is true for any value of x, so the possible values of x are all real numbers.

To be a valid rectangle, the length and width must both be positive.

So, we equate the expressions for the length and width of the rectangle greater than 0 and solve for x:

x > 0 and x - 2 > 0

x > 2,

Therefore, the possible values of x are all real-numbers greater than 2.

Part(b) :

The side of square is = (x-1),

So, it's area is represented by : (x-1)² = x² - 2x + 1;

The rectangle's length is : (x) units,

The rectangle's width is : (x-2) units,

So, the area will be = x(x-2) = x² - 2x,

We see that, the area of the square has a greater area than the rectangle,

Part (c) :

The difference in both areas will be calculated as : Area of Square - Area of rectangle;

(x² - 2x + 1) - (x² - 2x) = 1 units.

Therefore, the difference is 1 units.

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The given question is incomplete, the complete question is

A square has sides that are (x-1) units long and a rectangle has a length of x units and a width of (x-2) units;

(a) What are the possible values of x?

(b) does the square or the rectangle have the greater area?

(c) What is the difference in the areas?

Logistic growth function with oscillation is a mathematical model that describes the growth of a population that is limited by its resources.

The logistic growth function itself is an S-shaped curve that levels off as the population approaches its carrying capacity. However, when there are additional factors that cause oscillations or fluctuations in the population size, the model can be modified to include periodic behavior.

One example of a logistic growth function with oscillation is the Lotka-Volterra predator-prey model. In this model, the population of predators and prey are linked through a set of differential equations that describe how the two populations interact with each other. The oscillations in this model occur due to the interplay between the predator and prey populations, with each population affecting the growth of the other.

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The option B) yields the highest value for Z, which is 56.5. Therefore, the correct answer is B) x1 = 5, x2 = 5.25, Z = 56.5

To determine the correct answer, we can substitute each option into the objective function and check if the constraints are satisfied. Let's evaluate each option:

A) x1 = 5, x2 = 4.63, Z = 52.78

Checking the constraints:

17x1 + 8x2 = 17(5) + 8(4.63) = 85 + 37.04 = 122.04 ≤ 136 (constraint satisfied)

3x1 + 4x2 = 3(5) + 4(4.63) = 15 + 18.52 = 33.52 ≤ 36 (constraint satisfied)

B) x1 = 5, x2 = 5.25, Z = 56.5

Checking the constraints:

17x1 + 8x2 = 17(5) + 8(5.25) = 85 + 42 = 127 ≤ 136 (constraint satisfied)

3x1 + 4x2 = 3(5) + 4(5.25) = 15 + 21 = 36 ≤ 36 (constraint satisfied)

C) x1 = 5, x2 = 5, Z = 55

Checking the constraints:

17x1 + 8x2 = 17(5) + 8(5) = 85 + 40 = 125 ≤ 136 (constraint satisfied)

3x1 + 4x2 = 3(5) + 4(5) = 15 + 20 = 35 ≤ 36 (constraint satisfied)

D) x1 = 4, x2 = 6, Z = 56

Checking the constraints:

17x1 + 8x2 = 17(4) + 8(6) = 68 + 48 = 116 ≤ 136 (constraint satisfied)

3x1 + 4x2 = 3(4) + 4(6) = 12 + 24 = 36 ≤ 36 (constraint satisfied)

From the calculations above, we see that options B), C), and D) satisfy all the constraints. However, option B) yields the highest value for Z, which is 56.5. Therefore, the correct answer is: B) x1 = 5, x2 = 5.25, Z = 56.5.

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From the statements that are provided in the question, the statement that best describes when the plans  is Each plan utilizes a combination of 2 strength-training sessions and 3 aerobic exercise sessions per week.

A word problem are sentences describing a real-life scenario where a problem needs to be solved by mathematical calculation.

Ideally, for the best health benefits, such as increasing strength and aerobic and reduction in heart diseases, it is suggested to do a combination of strength training and aerobic training for at least five times a week.

Each plan utilizes a combination of 2 strength-training sessions and 3 aerobic exercise sessions per week. is the correct statement

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The perimeter of one face of the cube is given by the option (A) a/4.


The surface area of a cube is given by the formula 6a^2, where a is the length of one side of the cube. In the given expression 6(a/4)^2, we can simplify it as follows:
6(a/4)^2 = 6(a^2/16) = (6/16) * a^2 = 3/8 * a^2

We know that the perimeter of a square is equal to 4 times the length of one side. In this case, we have a cube, and each face of the cube is a square. Therefore, the perimeter of one face of the cube is 4 times the length of one side.

Hence, the correct option is (A) a/4, as it represents the perimeter of one face of the cube.

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Answer:

0 i think

Step-by-step explanation:

Answer:

1.68

Step-by-step explanation:

Answer:

x>24.75

Step-by-step explanation:

The given equation is :

\(\dfrac{-2}{5}x-9<\dfrac{9}{10}\)

Add 9 to both sides of the inequality.

\(\dfrac{-2}{5}x-9+9<\dfrac{9}{10}+9\\\\\dfrac{-2x}{5}<9.9\)

Multiply 5 to both sides of the inequality.

\(\dfrac{-2x}{5}\times 5<9.9\times 5\\\\-2x<49.5\)

Dividing both sides by(-2)

\(x<-24.75\)

or

\(x>24.75\)

Hence, the value of x is greater than 24.75.

We can conclude that gcd(a, b) divides 15 if and only if there exist integers s and t such that as + bt = 15.

If there are integers s and t such that as + bt = 15, then we can conclude that gcd(a, b) divides 15. This is known as Bézout's identity, which states that for any two integers a and b, there exist integers s and t such that as + bt = gcd(a, b).

To see why this is true, consider the set of all linear combinations of a and b, that is, the set {ax + by : x, y are integers}. This set contains all multiples of gcd(a, b) since gcd(a, b) divides both a and b.

Therefore, gcd(a, b) is the smallest positive integer that can be expressed as a linear combination of a and b.

Now, if as + bt = 15, then 15 is a linear combination of a and b, which means that gcd(a, b) divides 15.

Conversely, if gcd(a, b) divides 15, then we can find integers s and t such that as + bt = gcd(a, b), and we can scale this equation to obtain as' + bt' = 15, where s' = (15/gcd(a, b))s and t' = (15/gcd(a, b))t.

Therefore, we can conclude that gcd(a, b) divides 15 if and only if there exist integers s and t such that as + bt = 15.

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Answer:

x is equal to 4/3 ........

The value for the hotspots of the similar triangles ∆ABC and ∆PWR are:

(1). angle B = 68°

(2). PQ = 5cm

(3). BC = 19.5cm

(4). area of ∆PQR = 30cm²

Similar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.

(1). angle B = 180 - (22 + 90) {sum of interior angles of a triangle}

angle B = 68°

Given that the triangle ∆ABC is similar to the triangle ∆PQR.

(2). PQ/7.5cm = 12cm/18cm

PQ = (12cm × 7.5cm)/18cm {cross multiplication}

PQ = 5cm

(3). 13cm/BC = 12cm/18cm

BC = (13cm × 18cm)/12cm {cross multiplication}

BC = 19.5cm

(4). area of ∆PQR = 1/2 × 12cm × 5cm

area of ∆PQR = 6cm × 5cm

area of ∆PQR = 30cm²

Therefore, the value for the hotspots of the similar triangles ∆ABC and ∆PWR are:

(1). angle B = 68°

(2). PQ = 5cm

(3). BC = 19.5cm

(4). area of ∆PQR = 30cm²

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Answer:

17

Step-by-step explanation:

12 1/2-(-4 1/2)

12 1/2+ 4 1/2

17